Electrical multiplier using hall effect



Oct. 23, 1956 GQ HOLLINGSWORTH 2,767,911

ELECTRICAL MULTIPLLER 'USING' HALL EFFECT Filed Nom-'21, 1952 United States Patent O ELECTRICAL MULTIPLIER USING HALL EFFECT Guilford L. Hollingsworth, Seattle, Wash., assignor to Boeing Airplane Company, Seattle, Wash., a corporation of Delaware Application November 21, 1952, Serial No. 321,758

4 Claims. (Cl. 23S-61) This invention relates to apparatus for performing multiplication of two electrical quantities, and more particularly to such apparatus utilizingl the so-called Hall effect. The invention is herein illustratively described by reference to the preferred form thereof, but it will be understood thatr certain variations therein may be employed without departing from the inventive concepts.

Numerous devices have been proposed and used in the past to perform the mathematical operation of multiplying two independent variables, in the form of or convertible into voltages or currents, and for some applications certain of these devices were quite satisfactory. However, few if any, have been capable of fully satisfying the stringent requirements of a growing number of specialized applications including instantaneously acting computers and other high-precision electronic apparatus.

An example of a former type of electrical multiplier is the type utilizing a multigrid vacuum tube such as a pentode and applying the two variable quantities as voltages to separate control elements of the tube. However, the circuits of such a device are known to be relatively complex, exacting as to circuit design, calibration and adjustment, subject to change of characteristics with replacement of one multigrid vacuum tube for another, non-linear due to the varying non-linearv gain characteristics of all vacuum tubes, instable in operation under changing extraneous conditions, lacking `in capability of producing a, zero product, thereby requiring subtraction from the result of one multiplied quantity when the other quantity becomes zero, which leads to large-percentage errors because of the necessity sometimes of subtracting one large number fromv another, inability to multiply quantities of variable sign algebraically, and possessed of a rather large time constant causing lag in the sensitivity of the apparatus to sudden changes in either of the quantities being multiplied.

The general object of the present invention is to provide an electrical multiplier which overcomes the foregoing difculties to a large extent.

Use of the Hall effect to provide an alternating current volt-ampere meter is disclosed in the patent to Warner, No. 2,585,707, February l2, 1952, and of course essentially involves the performance of multiplication. Miller et al. Patent No. 2,543,640, February 27, 1951, also utilizes the Hall eifect in a circuit which essentially multiplies electrical quantities. These two patents appear to vrepresent. the present state of development in the art of electrical multipliers in which the Hall effect is employed.

While for certain limited applications,y or within loose standards of precision, the simple or basic Hall effect multiplying arrangement embodied in lthe foregoing two patents would be satisfactory, it has been found in practice that the inevitable non-linearity in the relationship between the magnetic iield strength applied to the Hall elfect strip and the magnetizing force applied to the electromagnet precludes its application, in that form,V

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.to many high-precision systems of modern design. The present invention in essence provides a novel and highly effective means of eliminating Ythat source of error from the' basic Hall effectr multiplier without rendering the same any `the less attractive from any of the various other standpoints enumerated above.

As illustratively described herein, the invention accomplishes that result by interposing a second Hall effect strip, preferably similar in form and location to the normal multiplier strip, in the air gap of the electromagnet, energizing. this second strip with a predetermined or constant reference current and applying the output Hall effect voltage thus produced in the second strip as negative feedback to the electrical circuit by which magnetizing force for the magnet is generated as a direct function of one of the electrical variables to be multiplied by the other.

These and other features, objects and advantages of the present invention, including aspects of the preferred example thereof, will become more fully evident from the following description by reference to the accompanying drawings.

Figure l is a diagram illustrating `the principle involved iny the sc-called Hall elect.

Figure 2 is a schematic diagram of a Hall effect multiplier embodying the present invention.

The Hall effect exhibited by metals as depicted in Figure l utilizes a thin metal strip placed in a magnetic field H with the plane of the strip disposed perpendicular to the magnetic lines of force. An electric current l passed through the strip in a direction perpendicular to the lield then produces a potential gradient in the strip in a direction transverse both to the magnetic lield and to the direction of current flow. It is found that the vol-tage VH developed across the strip in this manner is a direct linear function of the product of the instantaneous magnetic li'eld strength and the instantaneous magnitude of the electric current. Variation of either the current I or the lield H in magnitude produces a proportional magnitude variation of voltage VH, while reversal of the polarity or direction of either of these controlling variables produces a corresponding reversal of polarity of voltage VH.

Thus it becomes readily possible to multiply algebraically two voltages, two currents or a current and a voltage if the strength of the magnetic field is varied in proportion to one of these variables and the current in the Hall effect strip represents the other variable.

However, in the simple embodiment of that principle in a mathematical multiplier of electrical quantities certain inaccuracies are inherent whichA cannot be tolerated in various important applications and have not been overcome in the past to permit using Hall eliect multipliers in those cases. These inaccuracies arise chieily from the nonlinearity -in the variation of the magnetic field strength as a function of the control voltage or current which produces ythe magnetizing force or to which the magnetizing force is made proportional. ln order to produce a strong magnetic field H capable of generating an appreciable product voltage VH by the Hall effect in such a multiplier a high-permeability electromagnet is essential, an air-core magnetic field coil being usually inadequate, and this of course involves a magnetization characteristic with Vinevitable departures from strict linearity.

The present invention provides an effective solution to that problem Without creating objectionable complexities nor reducing the other inherent advantages of a Hall effect multiplier over other types. This is accomplished preferably in the manner shown schematically in Figure 2, which illustrates the principle of the invention applied to Hall effect apparatus for multiplication of two direct voltages A and B to produce a product voltage C.

In that figure the usual Hall effect strip is placed in the airgap between the poles of the electromagnet 12 having a magnetizing coil 12. Energizing current for this coil is supplied by a voltage-controlled current generator 14 the output of which is made as nearly a linear function of applied voltage A as it can be. For greatest versatility of the apparatus this current generator is capable of responding to an applied voltage A of either polarity and of preserving the sign of that voltage in terms of direction of current flow produced in coil 12', hence of the direction of magnetic eld H passing through strip 10. Preferably current generator 14 is in the form of an electronic amplifier of suitable design capable of receiving connections for negative feedback for a purpose to be described.

The Hall effect strip 10 is subjected, through suitable connections, to the passage of a direct current I proportional to applied voltage B. The output voltage C (or VH) derived from strip 10 through suitable connections is then the product of A times B. The voltage controlled current generator 16 producing the current I is preferably similar to the current generator 14 in that it is made capable of responding to an applied voltage of either polarity and of preserving the sign of that voltage in terms of the direction of current ow produced in the strip 10. The current generator 16 is or should be designed for substantially linear operation so as to preserve the direct proportionality between voltage B and current I.

The elements thus far enumerated and described in connection with Figure 2 are already known to the art and provide an electrical multiplier having important advantages over other types, but one which is subject to the inaccuracies mentioned above. According to this invention a second Hall effect strip 18 is inserted in the airgap of magnet 12 where it is subjected to the magnetic field H like the strip 10. The strip 18 is also subjected to the passage of a constant direct current I', a reference current, of predetermined value, hence produces a Hall effect output voltage Vn' which is proportional to the produce of this current and the strength of magnetic field H. Preferably strip 18 is made similar to strip 10 and is so arranged in the magnet gap that it is subjected to the field H, and variations therein, in a manner identical to strip 10, to exhibit identical Hall effect properties.

The Hall effect voltage Vn of the second strip 18 is applied as negative feedback to the current generator 14, as indicated by the conductor 20. By suitable provisions involving well known amplifier design considerations this negative feedback voltage derived by Hall effect strip 18 and applied to amplifier 14 cancels out any nonlinearities in the gain or amplification characteristic of the entire amplifier channel between the points of derivation and application of the negative feedback voltage, so that the overall effective gain of that channel is substantially independent of any nonlinear effects in the system between those points, including nonlinearities due to the Hall effect itself. It will be noted that electromagnet 12 is itself located between such points. Consequently that fraction of the negative feedback voltage derived by the second Hall effect strip 18 as a result of magnetic field H, when fed to amplifier 14 produces a corrective action therein which cancels out any nonlinearities in the niagnetizing curve of magnet 12. In other words, because of feedback voltage Vn the multipliers accuracy is no longer back voltage VH applied to amplifier 14. By supplying this current from a constant current generator 22 which is adjustable as to its output current, therefore, the percentage of negative feedback supplied in that manner may be conveniently adjusted to the desired value. Other ways of accomplishing the same end result will be obvious to those skilled in the art. Such feedback adjustment also affords a convenient means of applying a constant multiplying factor to the system, since changes in feedback to amplifier 14 change its gain and hence the product or output of the system as a multiplying device.

By applying voltages A and B to the respective current generators 14 and 16 the Hall effect strip 10 is subjected to the proportionally related magnetic field H and energizing current I, and produces an output voltage VH representing the product of voltages A and B. Moreover such product voltage is the algebraic product inasmuch as it depends for polarity upon the respective polarities of both applied voltages. Moreover, should one of the voltages A or B become zero, the product voltage Vn will likewise become zero and it will be unnecessary to perform a subtraction of some constant voltage from the product to achieve that result as in some other types of multipliers. The time-constant of the device is extremely low as to the variations of voltage B, but the finite magnetic inductance of coil 12' prevents as rapid response of output voltage to variations of applied voltage A. In many precision multiplier applications, however, it is sufficient if the time-constant be short as to one of the multiplied values even though not as to the other. In these and all other important respects the normal advantages of a Hall effect multiplier are fully preserved l intact even with the provision of the second Hall effect strip 18 and negative feedback overcoming nonlinearities inherent in the electromagnet and amplifier 14 in accordance with this invention.

The invention has been described by reference to p the preferred embodiment thereof as applied to multiplication of direct voltages. It should be understood, however, that the principles involved are likewise applicable to multiplication of alternating voltages or of a direct voltage and an alternating voltage. The same applies to the multiplication of currents or of a current by a voltage because of the simple expedients available for transforming from current to voltage and the reverse. In fact there is reason for employing alternating current for the current I if extreme precision is desired because the magnetically produced defiection of the current fiow in the strip 10 results in thermal gradients in the strip parallel to the product voltage vector VH (due to Von Ettinghausen effect) and tends to change the value of such voltage. For that reason it may be preferred in some instances to convert from direct voltage A into alternating current (I) and then, if necessary, convert the resultant alternating product or output voltage (VH) back into direct voltage, preferably by means of a phase-sensitive detector Which is capable of rejecting or avoids converting induced voltages due to the magnetic field. Another advantage of this conversion to alternating current is that amplifier 16 and a utilization circuit connected to C" can be A. C. coupled, with consequent freedom from drift occurring in D. C. amplifiers.

These and other departures from the details of illustration in the practice of the invention will be understood by those skilled in the art as falling within the inventive concepts intended to be defined by the claims which follow.

I claim as my invention:

l. Apparatus for Vmultiplying together two electrical quantities, comprising, in combination with Hall effect multiplying means including an electromagnet, current generating means for energizing said magnet in proportion to one of said quantities, a Hall effect strip disposed in the field of said electromagnet, substantially perpendicular to the magnetic lines of force thereof, means for passing Hall effect strip energizing current through said strip in proportion to the other of said quantities, and means deriving the resultant Hall effect product voltage from said strip, a second Hall effect strip disposed in the field of said electromagnet substantially perpendicular to the magnetic lines of force thereof, means for passing Hall eiect strip current through said second strip and means deriving the resultant Hall eiect product voltage from said second strip and applying said latter product voltage as negative feedback to said current generating means to reduce multiplication inaccuracies in said first Hall eiect strip due to non-linearities in said electromagnet energized by said current generating means.

2. Apparatus dened in claim 1, wherein the second and rst Hall eect strips are similar and are similarly arranged in relation to the electromagnet.

3. In combination with Hall elect electrical multiplying apparatus including amplifier means for energizing the Hall effect electromagnet in accordance with one of the multiplied quantities, a second Hall eiect strip disposed in the eld of such electromagnet substantially perpendicular to the magnetic lines of force thereof, current supply means passing Hall eEect strip energizing current through said second Hall eiect strip, and means deriving the resultant Hall effect product voltage from said second strip and connected` to said amplier means operatively for reducing the gain of said amplifier means dynamically substantially in proportion to said voltage.

4. The" combination defined in claim 3, wherein the current supply means is adjustable as a means of varying the gain-reducing elcct of the derived voltage in the amplier means.

References Cited in the le of this patent UNITED ASTATES PATENTS 1,596,558 Sokolof Aug. 17, 1926 1,810,539 Sokolotf June 16, 1931 1,948,209 Finchander Feb. 20, 1934 2,464,807 Hansen Mar. 22, 1949 2,585,707 Warner Feb. 12, 1952 2,594,939 Leete Apr. 29, 1952 FOREIGN PATENTS 624,036 Great Britain May 26, 1949 

